Matrix factorization

In this section, we're going to look into recommender systems and introduce matrix factorization techniques. In typical collaborative filtering problems, we have users along one axis and items or offers along the other axis. We want to solve for the predicted rating for a user for any given item, but to get there we have to somehow compute the affinity between the users or the item. In the previous section, we looked at item-to-item collaborative filtering, where we explicitly computed the similarity matrix using the cosine similarity metric, but now we want to explore a method that's not going to explicitly compare items to items or users to users.

Matrix factorization is a form of collaborative filtering that focuses on the intangibles of products. At a conceptual level, every product or restaurant, for example, has intangibles that cause you to like, dislike, or remain indifferent toward them. For example, for a restaurant, maybe the atmosphere or the vibe you get...